The harmonic ensemble similarity method treats the conformational ensemble within each trajectory as a high-dimensional Gaussian distribution \(N(\mu, \Sigma)\). The mean \(\mu\) is estimated as the average over the ensemble. The covariance matrix \(\Sigma\) is calculated either using a shrinkage estimator (cov_estimator='shrinkage') or a maximum-likelihood method (cov_estimator='ml').

The harmonic ensemble similarity is then calculated using the symmetrised version of the Kullback-Leibler divergence. This has no upper bound, so you can get some very high values for very different ensembles.

It is recommended that you align your trajectories before computing the harmonic similarity. You can either do this yourself with align.AlignTraj, or pass align=True into encore.hes. The latter option will align each of your Universes to the current timestep of the first Universe. Note that since encore.hes will pull your trajectories into memory, this changes the positions of your Universes.